InterviewSolution
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InterviewSolution
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The line `lx+my+n=0` is a normal to the parabola `y^2 = 4ax` ifA. ` (( -n ) /(l ) , ( - 2am ) /( l)) `B. ` ( ( -n ) /(l) , ( 2am )/( l) ) `C. ` ( ( n ) / ( l) , ( - 2am )/ ( l)) `D. ` (( n ) /( l) , ( 2am ) /( l)) ` |
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Answer» Correct Answer - C Tangent of the parabola ` y^ 2 = 4ax ` at point ` P ( x_ 1, y _ 1 ) ` is ` yy _ 1 = 2a ( x +x _ 1 ) ` `rArr 2a x _ 1 - yy _ 1 + 2ax = 0 " " ` … (i) Which is also equation of the polar of the parabola `y ^ 2 = 4ax ` . Same as the line ` lx + my + n = 0 " " `... (ii) On comparing both lines, we get ` ( 2a)/ (l ) = ( - y ) /( m) = ( 2ax ) /( n ) ` Taking first two parts ` ( y = - ( 2am ) / ( l)) ` Taking first and last parts, ` ( x = ( n ) / ( l) ) ` ` therefore ` Required pole of the line is ` { ( n ) / (l) , ( - 2am ) /(l) } `. |
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